Recursive Tree Research Articles

Correlation between telomerase reverse transcriptase messenger RNA expression and survival of patients with papillary thyroid carcinoma

BackgroundTelomerase reverse transcriptase promoter mutations were recently found to be associated with poorer prognosis in patients with papillary thyroid carcinoma. Correlation between telomerase reverse transcriptase messenger RNA expression and survival of patients with papillary thyroid carcinoma has not been determined. MethodsClinical information, somatic mutations, and RNA sequencing of 492 papillary thyroid carcinoma patients were obtained from The Cancer Genome Atlas. Correlations between messenger RNA expression and clinicopathologic variables were evaluated. Recursive partitioning regression trees were used to find cutoffs predicting survival. Differentially expressed gene analysis was performed by Edge-R, and Database for Annotation, Visualization and Integrated Discovery 6.7 was used to pathway analysis. ResultsTelomerase reverse transcriptase messenger RNA expression was positively correlated with stages II and IV and high MACIS Prognostic Score for Papillary Thyroid Carcinoma. Using a telomerase reverse transcriptase messenger RNA level of 2.854 as a cutoff, patients with higher telomerase reverse transcriptase messenger RNA expression showed poorer overall survival (hazard ratio = 20.7). The higher telomerase reverse transcriptase messenger RNA group showed upregulation of 2,255 genes, with enrichment of carcinogenic pathways. ConclusionHigher telomerase reverse transcriptase messenger RNA expression was associated with poorer survival in patients with papillary thyroid carcinoma and was a better predictor for death than telomerase reverse transcriptase promoter mutations. Measuring telomerase reverse transcriptase messenger RNA expression in thyroid cancer tissue may allow early identification of papillary thyroid carcinoma patients with worse overall survival.

Untangling genotype x management interactions in multi-environment on-farm experimentation

• Identifying optimum crop design to match the environment remains a useful concept to maximise crop yields and farmers’ profits. • There is opportunity for field agronomic multi-environment experimentation to embrace system research approaches. • The value of applying a GxExM framework to increase yields and manage risks relates to our capacity to predict E at sowing and to the genetic diversity of the germplasm. Identifying optimum combinations of genotype (G) and agronomic management (M) i.e. crop design, to match the environment (E) i.e. site and expected seasonal conditions, is a useful concept to maximise crop yields and farmers’ profits. However, operationalising the concept requires practitioners to understand the likelihood of different E outcomes and GxM combinations that would maximise yields while managing risks. Here we propose and demonstrate an analysis framework to inform crop designs (GxM) at the time of sowing of a dryland maize crop, that combines data sets from multi-environment field experimentation and crop simulation modelling, and that accounts for risk preference. A network of replicated, G by M on-farm and on-research station trials (n = 10), conducted across New South Wales and Queensland, Australia, over three seasons (2014–2016) was collected. The trials consisted of combinations of commercial maize hybrids, sown at a range of plant densities and row configurations producing site average yields (Environment-yield) that varied between 1576 and 7914 kg ha −1 . Experimental data were used to test the capacity of APSIM-Maize 7.10 to simulate the experimental results, and to in-silico create a large synthetic data set of multi-E (sites x seasons) factorial combination of crop designs. Data mining techniques were applied on the synthetic data set, to derive a probabilistic model to predict the likely Environment-yield and associated risk from variables known at sowing, and to derive simple “rules of thumb” for farmers that discriminate high and low yielding crop designs across the lower, middle and upper tercile of the predicted Environment-yields. Four risk profiles are described, a “Dynamic” (i.e. each year the farmer would adopt a crop design based on the predicted Environment-yield tercile and corresponding “rules of thumb”), “High rewards seeker” (i.e. each year the farmer would adopt the crop design that optimises yield for the higher tercile of Environment-yields), “Middle’er” (i.e. each year the farmer would adopt the crop design that optimises yield for the middle tercile of Environment-yields), and “Risk averse” (i.e. each year the farmer would adopt the crop design that optimises yield for the lower tercile of Environment-yields). The difference in yield between the lowest and highest performing crop design was ca. 50 % which translates into a ca. 2-fold change in water use efficiency, i.e. from 8 to 15 kg grain mm −1 rainfall. APSIM-Maize explained 88 % of the variability in the experimental data set. The validated model was used to extend the number of E sampled by adding additional sites within the same region and using historical climate records for the period 1950–2018. Crop available water at the time of sowing was a good predictor for the likelihood of the season falling within each of the three Environment-yield terciles. Recursive partitioning trees showed that plant density and hybrid were the main variables discriminating crop performance within the upper, middle and lower terciles of Environment-yields. The probability distribution functions for yield resulting from the alternative risk management strategies were tested in terms of changes in the mean yield, an index of yield stability, and down-side risk i.e. the likelihood of achieving a non-economic yield. We conclude that (i) for dryland maize cropping, the crop water availability at the time of sowing can be used to inform optimum crop designs, increase yields and yield stability and reduce down-side risks; and (ii) the proposed framework is useful to untangle complex GxExM interactions in field experimentation that provide a transferable platform to develop simple rules to identify optimum crop designs early in the season.

Limit Theorems for the ‘Laziest’ Minimal Random Walk Model of Elephant Type

We consider a minimal model of one-dimensional discrete-time random walk with step-reinforcement, introduced by Harbola, Kumar, and Lindenberg (2014): The walker can move forward (never backward), or remain at rest. For each $n=1,2,\cdots$, a random time $U_n$ between $1$ and $n$ is chosen uniformly, and if the walker moved forward [resp. remained at rest] at time $U_n$, then at time $n+1$ it can move forward with probability $p$ [resp. $q$], or with probability $1-p$ [resp. $1-q$] it remains at its present position. For the case $q>0$, several limit theorems are obtained by Coletti, Gava, and de Lima (2019). In this paper we prove limit theorems for the case $q=0$, where the walker can exhibit all three forms of asymptotic behavior as $p$ is varied. As a byproduct, we obtain limit theorems for the cluster size of the root in percolation on uniform random recursive trees.

Structure‐aware 3D reconstruction for cable‐stayed bridges: A learning‐based method

AbstractA powerful deep learning‐based three‐dimensional (3D) reconstruction method for reconstructing structure‐aware semantic 3D models of cable‐stayed bridges is proposed herein. Typically, conventional bridge semantic 3D model reconstruction methods are not robust when low‐quality point clouds are used. Furthermore, they are suited particularly for their respective fields and less generalized for cable‐stayed bridges. Hence, a structure‐aware learning‐based cable‐stayed bridge 3D reconstruction framework is proposed. The encoder part of the network uses both multiview images and a photogrammetric point cloud as input, whereas the decoder part uses a recursive binary tree network to model a high‐level structural relation graph and low‐level 3D geometric shapes. Two actual cable‐stayed bridges are employed as examples to evaluate the proposed method. Test results demonstrate that the proposed method successfully reconstructs the bridge model with structural components and their relations. Quantitative results indicate that the predicted models achieved an average F1 score of 99.01%, a Chamfer distance of 0.0259, and a mesh‐to‐cloud distance of 1.78 m. The achieved result is similar to that obtained using the manual reconstruction approach in terms of component‐wise accuracy, and it is considerably better than that obtained using the manual approach in terms of spatial accuracy. In addition, the proposed recursive binary tree network is robust to noise and partial scans. The potential applications of the obtained 3D bridge models are discussed.

Asymptotic results on Hoppe trees and their variations

AbstractA uniform recursive tree on n vertices is a random tree where each possible $(n-1)!$ labelled recursive rooted tree is selected with equal probability. We introduce and study weighted trees, a non-uniform recursive tree model departing from the recently introduced Hoppe trees. This class generalizes both uniform recursive trees and Hoppe trees, providing diversity among the nodes and making the model more flexible for applications. We analyse the number of leaves, the height, the depth, the number of branches, and the size of the largest branch in these weighted trees.

ON SEVERAL PROPERTIES OF A CLASS OF PREFERENTIAL ATTACHMENT TREES—PLANE-ORIENTED RECURSIVE TREES

In this paper, several properties of a class of trees presenting preferential attachment phenomenon—plane-oriented recursive trees (PORTs) are uncovered. Specifically, we investigate the degree profile of a PORT by determining the exact probability mass function of the degree of a node with a fixed label. We compute the expectation and the variance of degree variable via a Pólya urn approach. In addition, we study a topological index, Zagreb index, of this class of trees. We calculate the exact first two moments of the Zagreb index (of PORTs) by using recurrence methods. Lastly, we determine the limiting degree distribution in PORTs that grow in continuous time, where the embedding is done in a Poissonization framework. We show that it is exponential after proper scaling.

The existence of a giant cluster for percolation on large Crump–Mode–Jagers trees

AbstractIn this paper we consider random trees associated with the genealogy of Crump–Mode–Jagers processes and perform Bernoulli bond-percolation whose parameter depends on the size of the tree. Our purpose is to show the existence of a giant percolation cluster for appropriate regimes as the size grows. We stress that the family trees of Crump–Mode–Jagers processes include random recursive trees, preferential attachment trees, binary search trees for which this question has been answered by Bertoin [7], as well as (more general) m-ary search trees, fragmentation trees, and median-of-( $2\ell+1$ ) binary search trees, to name a few, where to our knowledge percolation has not yet been studied.

Feature Selection Using Genetic Algorithms for the Generation of a Recognition and Classification of Children Activities Model Using Environmental Sound

In the area of recognition and classification of children activities, numerous works have been proposed that make use of different data sources. In most of them, sensors embedded in children’s garments are used. In this work, the use of environmental sound data is proposed to generate a recognition and classification of children activities model through automatic learning techniques, optimized for application on mobile devices. Initially, the use of a genetic algorithm for a feature selection is presented, reducing the original size of the dataset used, an important aspect when working with the limited resources of a mobile device. For the evaluation of this process, five different classification methods are applied, k-nearest neighbor (k-NN), nearest centroid (NC), artificial neural networks (ANNs), random forest (RF), and recursive partitioning trees (Rpart). Finally, a comparison of the models obtained, based on the accuracy, is performed, in order to identify the classification method that presents the best performance in the development of a model that allows the identification of children activity based on audio signals. According to the results, the best performance is presented by the five-feature model developed through RF, obtaining an accuracy of 0.92, which allows to conclude that it is possible to automatically classify children activity based on a reduced set of features with significant accuracy.

Abstract TP417: An Autoregulation-Derived Prediction Model for Midline Shift After Ischemic Stroke

Introduction: Identification of patients likely to develop midline shift (MLS) after large-vessel occlusion (LVO) stroke is essential for appropriate triage and patient disposition. Studies have identified clinical and radiographic predictors of MLS, but with limited accuracy. Using an innovative assessment of cerebral autoregulation, we sought to develop an accurate predictive model for MLS. Methods: We prospectively enrolled 73 patients with LVO stroke. Beat-by-beat cerebral blood flow (transcranial Doppler) and arterial pressure (arterial catheter or finger photoplethysmography) were recorded within 24 hours of the stroke, and a 24-hour brain MRI was obtained to determine infarct volume and MLS. Autoregulatory function was quantified from pressure-flow relation via projection pursuit regression (PPR), allowing for characterization of 5 hemodynamic markers (Figure 1A). We assessed the predictive relation of autoregulatory capacity and radiological and clinical variables to MLS using recursive classification tree models. Results: PPR successfully quantified autoregulatory function in 50/73 (68.5%) patients within 24 hours of LVO ischemic stroke (age 63.9±13.6, 66% F, NIHSS 15.8±6.7). Of these 50 patients, most (78%) underwent endovascular therapy. Thirteen (26%) experienced 24-h MLS; in these patients, infarct volumes were larger (140.2 vs. 48.6 mL, P<0.001 ), and ipsilateral (but not contralateral) falling slopes were steeper (1.1 vs. 0.7 cm·s -1 ·mmHg -1 , P=0.001 ). Among all clinical, demographic, and hemodynamic variables, only two (infarct volume, ipsilateral falling slope) significantly contributed to prediction of MLS (accuracy 94%; Figure 1B). Conclusions: This predictive model of MLS wields translatable potential for triaging level of care in patients suffering from LVO ischemic stroke, but further research, including optimization of the PPR algorithm as well as prospective use of the predictive model, is needed.

The height of depth‐weighted random recursive trees

In this paper, we introduce a model of depth‐weighted random recursive trees, created by recursively joining a new leaf to an existing vertex . In this model, the probability of choosing depends on its depth in the tree. In particular, we assume that there is a function such that if has depth then its probability of being chosen is proportional to . We consider the expected value of the diameter of this model as determined by , and for various increasing we find expectations that range from polylogarithmic to linear.

Analysis of social network metrics based on the model of random recursive tree

Social network analysis can be defined as the method of examining social structures with the help of networks and graph theory.In this paper, we aim to develop a model which can replicate the features of social networks present in the real world, and can easily derivethe various characteristics associated with those networks. We define a model based on Random Recursive Tree (RRT) which is an extension to the Barabási-Albert model, capturing key features, such as the degree variance, the network diameter, the average path length, degree distribution etc. with respect to the size of the network and analyze the trends between these metrics. We then validate the proposed model by constructing various cascade trees with the help of a real-life social network, WeChat data-set.

Combination of Recursive and Recurrent Neural Networks for Aspect-Based Sentiment Analysis Using Inter-Aspect Relations

Sentiment analysis studies in the literature mostly use either recurrent or recursive neural network models. Recurrent models capture the effect of time and propagate the information of sentiment labels in a review throughout the word sequence. Recursive models, on the other hand, extract syntactic structures from the texts and leverage the sentiment information during training. There are only a few studies that incorporate both of these models into a single neural network for the sentiment classification task. In this paper, we propose a novel neural network framework that combines recurrent and recursive neural models for aspect-based sentiment analysis. By using constituency and dependency parsers, we first divide each review into subreviews that include the sentiment information relevant to the corresponding aspect terms. After generating and training the recursive neural trees built from the parses of the subreviews, we feed their output into the recurrent model. We evaluated our ensemble approach on two datasets in English of different genres. We achieved state-of-the-art results and outperformed the baseline study by a significant margin for both domains.

Recursive tree processes and the mean-field limit of stochastic flows

Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We consider interacting particle systems on the complete graph in the mean-field limit, i.e., as the number of vertices tends to infinity. We are not only interested in the mean-field limit of a single process, but mainly in how several coupled processes behave in the limit. This turns out to be closely related to recursive tree processes as studied by Aldous and Bandyopadyay in discrete time. We here develop an analogue theory for recursive tree processes in continuous time. We illustrate the abstract theory on an example of a particle system with cooperative branching. This yields an interesting new example of a recursive tree process that is not endogenous.

LP Relaxation and Tree Packing for Minimum $k$-Cut

Karger used spanning tree packings [D. R. Karger, J. ACM, 47 (2000), pp. 46--76] to derive a near linear-time randomized algorithm for the global minimum cut problem as well as a bound on the number of approximate minimum cuts. This is a different approach from his well-known random contraction algorithm [D. R. Karger, Random Sampling in Graph Optimization Problems, Ph.D. thesis, Stanford University, Stanford, CA, 1995, D. R. Karger and C. Stein, J. ACM, 43 (1996), pp. 601--640]. Thorup developed a fast deterministic algorithm for the minimum $k$-cut problem via greedy recursive tree packings [M. Thorup, Minimum $k$-way cuts via deterministic greedy tree packing, in Proceedings of the Fortieth Annual ACM Symposium on Theory of Computing, ACM, 2008, pp. 159--166]. In this paper we revisit properties of an LP relaxation for cͅut proposed by Naor and Rabani [Tree packing and approximating $k$-cuts, in Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, Vol. 103, SIAM, Philadelphia, 2001, pp. 26--27], and analyzed in [C. Chekuri, S. Guha, and J. Naor, SIAM J. Discrete Math., 20 (2006), pp. 261--271]. We show that the dual of the LP yields a tree packing that, when combined with an upper bound on the integrality gap for the LP, easily and transparently extends Karger's analysis for mincut to the $k$-cut problem. In addition to the simplicity of the algorithm and its analysis, this allows us to improve the running time of Thorup's algorithm by a factor of $n$. We also improve the bound on the number of $\alpha$-approximate $k$-cuts. Second, we give a simple proof that the integrality gap of the LP is $2(1-1/n)$. Third, we show that an optimum solution to the LP relaxation, for all values of $k$, is fully determined by the principal sequence of partitions of the input graph. This allows us to relate the LP relaxation to the Lagrangean relaxation approach of Barahona [Oper. Res. Lett., 26 (2000), pp. 99--105] and Ravi and Sinha [European J. Oper. Res., 186 (2008), pp. 77--90]; it also shows that the idealized recursive tree packing considered by Thorup gives an optimum dual solution to the LP.

On the independence number of some random trees

We show that for many models of random trees, the independence number divided by the size converges almost surely to a constant as the size grows to infinity; the trees that we consider include random recursive trees, binary and $m$-ary search trees, preferential attachment trees, and others. The limiting constant is computed, analytically or numerically, for several examples. The method is based on Crump–Mode–Jagers branching processes.

Effect of Smartphone Use on Intraocular Pressure

The rapidly increasing utilization of smartphones makes ophthalmic problems associated with their use an important issue. This prospective study aimed to determine whether using a smartphone to view visual material is associated with a change in the intraocular pressure (IOP), and to determine which groups of factors best predict the time-dependent increase in IOP with smartphone use. This study included 158 eyes (127 glaucomatous and 31 healthy eyes) recruited from Seoul National University Bundang Hospital. Participants performed a sustained fixation task consisting of watching a movie on a smartphone screen for 30 minutes continuously at a viewing distance of 30 cm. A small but statistically significant time-dependent increase in IOP was observed while viewing a movie on a smartphone, being 10.6 ± 3.1, 11.0 ± 3.3, 11.2 ± 3.4, and 11.6 ± 3.5 mmHg before and 5, 10, and 30 minutes after the fixation task, respectively (P < 0.0001). Recursive partitioning tree analysis revealed that a shallower anterior chamber (<2.32 mm) was the strongest predictive factor for faster time-dependent increase in IOP (0.68 mmHg/minute). A higher visual field mean deviation (≥–0.22 dB), and an older age (≥48 years) were the second and third most influential factors associated with the rate of IOP increase (0.59 and 0.15 mmHg/minute, respectively).

Dietary Determinants of Metabolic Syndrome Parameters Differ by Gender in College Students.

MyPlate is a guidance system for healthier eating choices. In this cross-sectional study, we investigated the influence of MyPlate food group consumption and exercise on metabolic syndrome (MetS) parameters in college students. Participant (n = 462) blood was analyzed using Cholestech for triglycerides (TG), glucose, low-density lipoprotein cholesterol (LDL-C), and high-density lipoprotein cholesterol (HDL-C). In addition, weight, waist circumference (WC), and blood pressure (BP) were measured. Diet and Wellness Plus was used to compute participant diet records. Regression analysis and a recursive decision tree were made to predict MetS using RStudio (V.1.1.463). BP decision tree predicted high risk of elevated blood pressure with a recall rate of 93.7%. For males; exercise, empty calories, dairy, and protein were main predictors. For females, vegetable and empty calorie consumption were primary determinants. HDL-C decision tree had a recall rate of 91.8% and showed that the main low HDL-C risk determinants for males were; exercise and grain consumption. Conversely, for females; empty calories, grain, and vegetable consumption were the key factors determining low HDL-C risk. This study shows that MyPlate recommendations are valuable to achieve adequate HDL-C and blood pressure and provides insight into the importance of tailoring food intake guidance based on gender.

Flattening Karatsuba’s Recursion Tree into a Single Summation

The recursion tree resulting from Karatsuba's formula is built here by using an interleaved splitting scheme rather than the traditional left/right one. This allows an easier access to the nodes of the tree and $2n-1$ of them are initially flattened all at once into a single recursive formula. The whole tree is then flattened further into a convolution formula involving less elementary multiplications than the usual Cauchy product. Unlike the traditional splitting scheme, the interleaved approach may also be applied to infinite power series, and corresponding formulas are also given.

Random tree recursions: Which fixed points correspond to tangible sets of trees?

Let be the set of rooted trees containing an infinite binary subtree starting at the root. This set satisfies the metaproperty that a tree belongs to it if and only if its root has children u and v such that the subtrees rooted at u and v belong to it. Let p be the probability that a Galton‐Watson tree falls in . The metaproperty makes p satisfy a fixed‐point equation, which can have multiple solutions. One of these solutions is p, but what is the meaning of the others? In particular, are they probabilities of the Galton‐Watson tree falling into other sets satisfying the same metaproperty? We create a framework for posing questions of this sort, and we classify solutions to fixed‐point equations according to whether they admit probabilistic interpretations. Our proofs use spine decompositions of Galton‐Watson trees and the analysis of Boolean functions.

Narrative Indicators of Adolescents’ Maladaptive Cognitive Schemas

Introduction. The article presents the results of a study of adolescents` personal narratives. The general aim of the study was to identify narrative indicators of adolescents’ maladaptive cognitive schemas. This aim was achieved by virtue of realization of such tasks as: to identify the specific text categories (indicators) that indicate the maladaptive schemas and to determine the predictive power of each category (indicator). In the course of theoretical analysis, there were systematized the approaches to the understanding of personal narratives and “self-texts”. There also was generalized the concept of maladaptive cognitive schemas, and were defined textual categories which can be reflected in the narratives of people who have certain maladaptive schemas.&#x0D; Methods. The methods of the empirical study were Dusseldorf Illustrated Schema Questionnaire for Children and the content-analysis of personal narratives. Statistical processing of the obtained data and determination of the predictive power of each narrative category were performed with the help of the method of recursive division trees.&#x0D; Results. As a result of the empirical study was it was found that certain categories in the personal narratives of adolescents allow us to predict the manifestation of individual maladaptive schemas. There were identified narrative indicators, able to predict fourteen of the eighteen schemas. It was determined that the knowledge of narrative indicators of maladaptive cognitive schemas can be used within the psychological counseling and therapy at the stage of gathering primary information, as well as in the context of purposeful psychological impact.&#x0D; Conclusions. There were described the topical prospects for further scientific development of the problem, which were to expand the categorical structure of content analysis, which would allow to find indicators of four schemas that remain unclear, as well as to widen the age range of respondents and to test the hypothesis about the existence of a link between the personal narratives of adults and their maladaptive schemas. There was made an assumption that modification of a personal narrative can accelerate therapeutic work aimed at eliminating the negative impact of maladaptive schemas on a person's life.